1. De Broglie Waves, Uncertainty, and Atoms
Physics 102: Lecture 23
De Broglie Waves, Uncertainty, and Atoms
Hour Exam 3
Monday, April 14
Covers
lectures through Lecture 20 (last Monday’s lecture)
homework through HW 10
discussions through Disc 10
Review, Sunday April 13, 3 PM, 141 LLP 1

2. Hour Exam 3 Review Fall 2007, HE2, problems 18-25
Fall 2007, HE3, all except 22,27

3. Photoelectric Effect Summary
Each metal has “Work Function” (W0) which is the minimum energy needed to free electron from atom.
Light comes in packets called Photons
E = h f h=6.626 X Joule sec
Maximum kinetic energy of released electrons
K.E. = hf – W0
All puzzles explained with quantum theory. 30

4. Photoelectric Effect Summary
Maximum kinetic energy of released electrons
K.E. = hf – W0 hf W0 KE
All puzzles explained with quantum theory. 30

5. Compton Scattering This experiment really shows photon momentum!
Pincoming photon + 0 = Poutgoing photon + Pelectron
Electron at rest
Outgoing photon has momentum p and wavelength 
Incoming photon has momentum, p, and wavelength l
Recoil electron carries some momentum and KE
Energy of a photon 5

6. Is Light a Wave or a Particle?
Electric and Magnetic fields act like waves
Superposition, Interference, and Diffraction
Particle
Photons
Collision with electrons in photo-electric effect
Compton scattering from electrons
BOTH Particle AND Wave

7. ACT: Photon Collisions
Photons with equal energy and momentum hit both sides of the plate. The photon from the left sticks to the plate, the photon from the right bounces off the plate. What is the direction of the net impulse on the plate?
1) Left 2) Right 3) Zero
Photon that sticks has an impulse p
Photon that bounces has an impulse 2p! 10

8. Radiometer
Incident photons
Black side (absorbs)
Shiny side (reflects)
Preflight 23.1
Photon A strikes a black surface and is absorbed. Photon B strikes a shiny surface and is reflected back. Which photon imparts more momentum to the surface?
Photon A Photon B
38% % 11

9. Ideal Radiometer
Photons bouncing off shiny side and sticking to black side. Shiny side gets more momentum so it should rotate with the black side leading 12

10. Our Radiometer
Black side is hotter:gas molecules bounce off it with more momentum than on shiny side-this is a bigger effect than the photon momentum 13

11. Are Electrons Particles or Waves?
Particles, definitely particles.
You can “see them”.
You can “bounce” things off them.
You can put them on an electroscope.
How would know if electron was a wave?
Look for interference!

12. Young’s Double Slit w/ electron
2 slits-separated by d
JAVA
Go to physics 2000 web site for JAVA version
Source of monoenergetic electrons L
Screen a distance L from slits 41

13. Electrons are Waves?
Electrons produce interference pattern just like light waves.
Need electrons to go through both slits.
What if we send 1 electron at a time?
Does a single electron go through both slits? 43

14. Electrons are Particles and Waves!
Depending on the experiment electron can behave like
wave (interference)
particle (localized mass and charge)
If we don’t look, electron goes through both slits. If we do look it chooses 1. 46

15. De Broglie Waves
So far only photons have wavelength, but De Broglie postulated that it holds for any object with momentum- an electron, a nucleus, an atom, a baseball,…...
Explains why we can see interference and diffraction for material particles like electrons!! 15

16. Preflight 23.3 Which baseball has the longest De Broglie wavelength?
31%
60% 8%
(1) A fastball (100 mph)
(2) A knuckleball (60 mph)
(3) Neither - only curveballs have a wavelength
Lower momentum gives higher wavelength.
p=mv, so slower ball has smaller p. 18

17. ACT: De Broglie Wavelength
A stone is dropped from the top of a building.
What happens to the de Broglie wavelength of the stone as it falls?
1. It decreases
2. It stays the same
3. It increases
Speed, v, KE=mv2/2, and momentum, p=mv, increase. 20

18. Comparison: Wavelength of Photon vs. Electron
Example
Comparison: Wavelength of Photon vs. Electron
Say you have a photon and an electron, both with 1 eV of energy. Find the de Broglie wavelength of each.
Equations are different - be careful!
Photon with 1 eV energy:
Big difference!
Electron with 1 eV kinetic energy:
Solve for 23

19. Preflights 23.4, 23.5
Photon A has twice as much momentum as Photon B. Compare their energies.
21%
47%
33%
EA = EB
EA = 2 EB
EA = 4 EB
and so
double p then double E
Electron A has twice as much momentum as Electron B. Compare their energies.
22%
40%
38%
EA = EB
EA = 2 EB
EA = 4 EB
double p then quadruple E 25

20. ACT: De Broglie
Compare the wavelength of a bowling ball with the wavelength of a golf ball, if each has 10 Joules of kinetic energy.
(1) lbowling > lgolf
(2) lbowling = lgolf
(3) lbowling < lgolf 27

21. Heisenberg Uncertainty Principle
Rough idea: if we know momentum very precisely, we lose knowledge of location, and vice versa.
This seems weird but…
OK this is weird but…… it is also true. 29

22. Heisenberg Uncertainty Principle: A Consequence of the Wave Nature of Particles
screen
Number of electrons arriving at screen w
Dpy = p sinq p q p q
electron beam
Dy = w
= l/sinq y x
Use de Broglie l 33

23. to be precise... Preflight 23.7
Of course if we try to locate the position of the particle along the x axis to Dx we will not know its x component of momentum better than Dpx, where
and the same for z.
Preflight 23.7
According to the H.U.P., if we know the x-position of a particle, we can not know its:
(1) y-position (2) x-momentum
(3) y-momentum (4) Energy
51% correct 35

24. Early Model for Atom Plum Pudding
positive and negative charges uniformly distributed throughout the atom like plums in pudding - +
But how can you look inside an atom m across?
Light (visible) l = 10-7 m
Electron (1 eV) l = 10-9 m
Helium atom l = m 38

25. Rutherford Scattering
Scattering He++ atoms off of gold. Mostly go through, some scattered back!
(Alpha particles = He++)
Flash
Only something really big (i.e. nucleus) could scatter the particles back!
If nucleus was baseball in Memorial Stadium, electrons would be
A) Front Row B) Back Row B) Quad C) Savoy D) Moon
Atom is mostly empty space with a small (r = m) positively charged nucleus surrounded by cloud of electrons (r = m) 42

26. Nuclear Atom (Rutherford)
Large angle scatterings
nuclear atom
Classic nuclear atom is not stable!
Electrons will radiate and spiral into nucleus
Need quantum theory 45

27. Recap Photons carry momentum p=h/l Everything has wavelength l=h/p
Uncertainty Principle DpDx > h/(2p)
Atom
Positive nucleus m
Electrons “orbit” m
Classical E+M doesn’t give stable orbit
Need Quantum Mechanics! 50

28. Reminder: Review Sunday